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Equation (2x-4)(x-11)+28=0
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Similar expressions
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(2x-4)(x-11)+28=0 equation
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The solution
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[src]
(2*x - 4)*(x - 11) + 28 = 0
$$\left(x - 11\right) \left(2 x - 4\right) + 28 = 0$$
Detail solution
Expand the expression in the equation
$$\left(x - 11\right) \left(2 x - 4\right) + 28 = 0$$
We get the quadratic equation
$$2 x^{2} - 26 x + 72 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 2$$
$$b = -26$$
$$c = 72$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 9$$
$$x_{2} = 4$$
$$\left(x - 11\right) \left(2 x - 4\right) + 28 = 0$$
We get the quadratic equation
$$2 x^{2} - 26 x + 72 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 2$$
$$b = -26$$
$$c = 72$$
, then
D = b^2 - 4 * a * c =
(-26)^2 - 4 * (2) * (72) = 100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 9$$
$$x_{2} = 4$$
Sum and product of roots
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sum
4 + 9
$$4 + 9$$
=
13
$$13$$
product
4*9
$$4 \cdot 9$$
=
36
$$36$$
36
The graph